Long story short, I've lost the anti-skating counterweight and can't find a replacement. I'm going to make one myself (a piece of metal hanging on a thread -- not exactly an ambitious DIY project) but what the weight of the stupid thing should be? I can't find any info...

I don't have a scale for such small weights, but if nobody else can
supply the info, I could try to measure mine and give you the
dimensions. Then your guess is as good as mine what metal it is.
BTW, is is the small weight, or the larger add-on one?

The arm on the TD166 allows the bias weight to be moved from almost zero distance to the pivot to about 40mm away (this from memory twenty years ago, plus armwaving). So who cares how precise the weight is? There's enough adjustment to cover it. As I recall, the weight is a cylinder of about 6.5mm diameter and the same height. It's probably made of steel or brass (more likely brass), but the density of both materials is very similar, and the weight (allowing for the hole through the middle) is likely to be about 1.8g. Hooray for physics!

Alternatively, you could just hang an arbitrary blob of Blutak on the end of a bit of fishing line, and use a test record to find the optimum amount.

If you want to be posh about it, make a thin-walled 8mm open aluminium cylinder on a lathe, and drill the closed end to 0.3mm, but fill the open end with as much or little plasticene or Blutak as necessary. Nobody can tell the difference from outside...

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The loudspeaker: The only commercial Hi-Fi item where a disproportionate part of the budget isn't spent on the box. And the one where it would make a difference...